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Let X be the graph of f(x) = r/ given below that is, X is the subset of R x R satisfying the given equation. . Define a bijective map g : X -R. Show that your map g is well-defined, injective, and surjective.

Let X be the graph of f(x) = r/ given below that is, X is the subset of R x R satisfying the given equation. . Define a bijective map g : X -R. Show that your map g is well-defined, injective, and surjective.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 10E
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Let X be the graph of f(x) = r2/3 given below that is, X is the subset of R x R satisfying the given equation. 1. Define a bijective map g : X → R. Show that your map g is well-defined, injective, and surjective. 2. Declare that a subset A of X is basic if A = Xn B,((r, y)) for some open ball B,((r, y)) = {(a, b) € R x R| V(I – a)² + (y – b)? < e}. Let Aj and A2 be basic subsets of X. i. Is Aj U Az a basic subset of X? ii. Is A N A, a basic subset of X? 3. In a similar manner, declare that a subset I of R is basic if I = RN B(r) for some open ball B.(r) = {a € R| |r – a| < e}. Given a basic subset A of X, is g(A) a basic subset of R? Justify your answer.
Transcribed Image Text:Let X be the graph of f(x) = r2/3 given below that is, X is the subset of R x R satisfying the given equation. 1. Define a bijective map g : X → R. Show that your map g is well-defined, injective, and surjective. 2. Declare that a subset A of X is basic if A = Xn B,((r, y)) for some open ball B,((r, y)) = {(a, b) € R x R| V(I – a)² + (y – b)? < e}. Let Aj and A2 be basic subsets of X. i. Is Aj U Az a basic subset of X? ii. Is A N A, a basic subset of X? 3. In a similar manner, declare that a subset I of R is basic if I = RN B(r) for some open ball B.(r) = {a € R| |r – a| < e}. Given a basic subset A of X, is g(A) a basic subset of R? Justify your answer.
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